Simplify the following expression: $k = \dfrac{40rt + 50t^2}{30st - 50rt} + \dfrac{30t^2 - 30t}{30st - 50rt}$ You can assume $r,s,t \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{40rt + 50t^2 + 30t^2 - 30t}{30st - 50rt}$ $k = \dfrac{40rt + 80t^2 - 30t}{30st - 50rt}$ The numerator and denominator have a common factor of $10t$, so we can simplify $k = \dfrac{4r + 8t - 3}{3s - 5r}$